Question

The state and local police departments are trying to analyze crime rates so they can shift their patrols from decreasing-rate areas to areas where rates are increasing. The city and county have been geographically segmented into areas containing 5,000 residences. The police recognize that not all crimes and offenses are reported: people do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of 800 of the 5,000 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area:

MONTH	CRIME INCIDENCE	SAMPLE SIZE	CRIME RATE
January	14	800	0.01750
February	14	800	0.01750
March	11	800	0.01375
April	15	800	0.01875
May	12	800	0.01500
June	14	800	0.01750
July	10	800	0.01250
August	9	800	0.01125
September	14	800	0.01750
October	7	800	0.00875
November	9	800	0.01125
December	12	800	0.01500

a. Determine the P−P− , S_p, UCL and LCL for a p-chart of 95 percent confidence (at Z = 1.96). (Round to 5 decimal places)

p bar:

Sp:

UCL:

LCL:

Answer 1

MONTH	CRIME INCIDENCE (np)	SAMPLE SIZE (n)	CRIME RATE (p = np/n)
Jan	14	800	0.01750
Feb	14	800	0.01750
Mar	11	800	0.01375
Apr	15	800	0.01875
May	12	800	0.01500
Jun	14	800	0.01750
Jul	10	800	0.01250
Aug	9	800	0.01125
Sep	14	800	0.01750
Oct	7	800	0.00875
Nov	9	800	0.01125
Dec	12	800	0.01500
		p_bar =	0.01469
		Sp =	0.00425
		UCL =	0.02302
		LCL =	0.00635